An estimate for multivariate interpolation
type: Item
instance of: scholarly article
title: An estimate for multivariate interpolation
zbMATH Open document ID: 0558.41008
DOI: 10.1016/0021-9045(85)90121-2
author: W. R. Madych
author: E. H. Potter
published in: Journal of Approximation Theory
publication date: 1985-01-01T00:00:00Z
review text: An estimate of the \(L^ p=L^ p(R^ n)\) norm of a function is given in terms of its values on a (not necessarily regular) grid of points and the \(L^ p\) norms of its k-th order derivatives, \(kp>n\). The result is useful in obtaining estimates for multivariate interpolation schemes; this is illustrated by an example involving generalized splines.
Mathematics Subject Classification ID: 41A05
Mathematics Subject Classification ID: 41A17
Mathematics Subject Classification ID: 41A63
zbMATH DE Number: 3890064
zbMATH Keywords: \(L^ p\)-estimates
zbMATH Keywords: multivariate interpolation schemes
zbMATH Keywords: example
zbMATH Keywords: generalized splines
MaRDI profile type: Publication
full work available at URL: 0021-9045(85)90121-2
OpenAlex ID: W4212887641
cites work: Equivalent Norms for Sobolev Spaces
cites work: Q5540873
cites work: Estimation of Linear Functionals on Sobolev Spaces with Application to Fourier Transforms and Spline Interpolation
cites work: General Lagrange and Hermite interpolation in \(R^n\) with applications to finite element methods
cites work: Q4110059
cites work: Q3215736
cites work: Scattered Data Interpolation: Tests of Some Method
cites work: Q4201228
cites work: Q3892772
cites work: Q3967921
cites work: Q4112362
description: scientific article; zbMATH DE number 3890064